Two demensional distributed feedback devices and lasers

ABSTRACT

Optical devices and waveguides using a thin film optical waveguide having a two dimensional array of perturbations associated therewith or with adjacent optically coupled layers. The array is regular and forms periodic variations in two noncoincident directions which serve to reflect or scatter light waves into controllable transverse modes of propagation. Lasers as well as passive devices are disclosed.

United States Patent Wang et al.

TWO DEMENSIONAL DISTRIBUTED FEEDBACK DEVICES AND LASERS Inventors: ShyhWang, El Cerrito; Sang K.

Sheem, Albany, both of Calif.

[ May 20, 1975 Primary Examiner-William L. Sikes Attorney, Agent, orFirm-Flehr, Hohbach, Test [57] ABSTRACT Optical devices and waveguidesusing a thin film optical waveguide having a two dimensional array ofperturbations associated therewith or with adjacent optically coupledlayers. The array is regular and forms periodic variations in twonon-coincident directions which serve to reflect or scatter light wavesinto controllable transverse modes of propagation. Lasers as well aspassive devices are disclosed.

14 Claims, 39 Drawing Figures j pmz'ria PEP 00/2 L 508577947?PEATUPBAr/aW D y-fl iicrip PAW/00m pitrueanr/a PATENTED HAY 2 01975SHEET DESOF 10 FIG- /6 PfP/OD/C Pawn/284710! KFEFZR'T/A/G MAM?!) I i I16- I819 MAP/POP Pmmmmm SHEET U70F 1O TWO DEMENSIONAL DISTRIBUTEDFEEDBACK DEVICES AND LASERS The invention herein described was made inthe course of research sponsored in part by the United States ArmyResearch Office.

BACKGROUND OF THE INVENTION This invention relates to thin film opticaldevices and lasers and more particularly to an improved form of suchdevices and lasers in which controllable transverse modes are obtainedusing a two-dimensional distributed feedback periodic structure.

Reference is made to my article entitled Proposal of periodic LayeredWaveguide Structures For Distributed Lasers", Journal of AppliedPhysics, Volume 44, Number 2, February 1973, pages 767-780 and to myprevious patent applications entitled (a) Thin Film Lasers, Ser. No.296,178 filed Oct. 10, 1972 and (b) Thin Film Optical Devices andLasers, Ser. No. 331,675 filed Feb.' 12, I973, which disclose aninvention relating to new classes of optical devices and lasers in whichperiodic variations are introduced in the structures of a thin filmoptical waveguide so as to create periodic reflections in the waveguide.These references are incorporated herein by reference. The periodicreflections thus generated give rise to distributed feedback(distributed coupling) between two counter running waves. In otherwords, the periodic variations in the waveguide structure of adistributed feedback laser serve a function similar to that of mirrorsin conventional lasers. The previous invention, as disclosed in thearticle and referenced patent applications, generally provide for aperiodic variation in a single or one dimensional arrangement in whichthe periodicity of the periodic variations used in the manufacture ofsuch devices must be maintained with considerable accuracy. This limitsthe usefulness of the previously disclosed optical devices and lasers tomaterials having a relatively broad gain profile or otherwise requiresthe imposition of strict manufacturing tolerances with attendant highcosts. There is a need, therefore, for a new and improved thin filmdevices and lasers. In addition, the previous invention provided anoutput beam in the form of a sheet of light which projects as a line onan intersecting plane. In many applications it is desirable to have apencil beam of light which would project as a spot on an intersectingsurface.

SUMMARY OF THE INVENTION AND OBJECTS In general it is an object of thepresent invention to provide a novel thin film optical devices andlasers which will overcome the above limitations and disadvantages.

A further object of the present invention is to extend the usefulness ofdistributed feedback devices and lasers.

A further object of the invention is to provide a thin film opticaldevices and lasers of the above character which are tunable by theapplication of acoustic or electric fields.

A further object of the invention is to provide a thin film opticaldevices of the above character which are particularly useful as passivedevices such as optical filters, modulators, and deflectors.

A further object of the invention is to provide a thin film opticaldevices and lasers of the above character in which the output is formedas a linear or pencil laser beam which will project as a spot on anintersecting surface.

In general, the foregoing objects and features of the invention areachieved by empolying a thin film optical waveguide structure defining aguided wavelength for propagating waves of light at a predeterminedfrequency in which the waveguide has a predetermined optical index ofrefraction and is made of a material transparent to light of apredetermined frequency. A boundary layer adjacent to said waveguide isin such proximity that the propagating wave for light at thepredetermined frequency extends both within said waveguide and into theboundary layer. The boundary layer has one or more indices of refractionat least a portion of which is less than the index of refraction of saidwaveguide. First means associated with one of said boundary layers andwaveguide or the interface between said boundary layer and saidwaveguide forms a periodic variation a, of an optical parameter in afirst direction, said periodic variation a, being arranged for causing aspatial variation of said optical parameter between two values whichrepeat in a regular pattern of predetermined periodicity. Second meansassociated with one of said boundary layers and waveguide or theinterface of the boundary layer and said waveguide forms a periodicvariation of an optical parameter thereof in a second direction. Thesecond periodic variation is arranged to cause spatial variation of thatoptical parameter between two values which repeat in regular pattern ofa second predetermined periodicity a wherein said periodicities a, and aare solutions to an equation of the general form (21r/A,)=F(N,,/a,,N,/a,) where A is the guided wavelength, N y and N areintegers and the ratios N la N la define an intersection in reciprocallattice space for a given waveguide structure. In this form the devicecan serve various passive functions such as filtering, modulation, anddeflection.

A laser is formed by making one of the waveguide or boundary layers of alaser active material which exhib' its gain to electromagnetic waves atthe feedback frequency.

A generalized form of the invention is disclosed when the periodicvariations are produced by perturbations such as a two dimensionalscattering array defining at least first and second periodic variationsa 0,. Such an array can be created by forming perturbations located atthe intersections of a pair of crossed gratings.

The structures of the present invention can be made by direct andpermanent physical modification of the layers of a bounded thin filmoptical waveguide or can be induced by acoustic, magnetic, or electricfields applied to optical waveguide or boundary layers thereof when thelater are constructed of suitable materials.

These and other objects and features of the invention will becomeapparent from the following decription and claims when taken inconjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE FIGURES FIG. 1 is a schematic representation ofa one dimensional distributed feedback structure constructed inaccordance with my previously referenced patent applications.

FIGS. 2A, 2B and 2C are schematic front, side and top plane views of atwo dimensional distributed feedback structure constructed in accordancewith the present invention.

FIG. 3 is a diagram plotting reciprocal lattice space for the structureof FIGS. 2.

FIG. 4 is a diagram illustrating operating points for the twodimensional distributed feedback laser of FIG. 2 in three dimensional kspace.

FIG. 5 is a diagram similar to that of FIG. 4 and showing the radiationmodes of a laser under a particular set of operating conditions.

FIGS. 6A and 6B and 7 are schematic views of a two dimensionaldistributed feedback structure constructed in accordance with thepresent invention in which the planes creating the feedback areseparated.

FIGS. 8 and 9 are schematic illustrations of other constructions of twodimensional distributed feedback structures constructed in accordancewith the present invention.

FIGS. 10A, 10B and 10C are exploded views illustrating various ways ofintroducing periodic pertrubations in the boundary layers and in thefilm.

FIGS. 11 and 12 show graphs of portions of reciprocal lattice space forparticular sets of conditions of operation of a two dimensionaldistributed feedback laser constructed in accordance with the presentinvention.

FIG. 13 is a top plane view schematically illustrating a dot scatteringarray two dimensional distributed feedback structure constructed inaccordance with the present invention.

FIG. 14 is a schematic cross-sectional view of an etched or hollow dotstructure taken generally along the reference lines A,B, of FIG. 13.

FIG. 15 is a schematic cross-sectional view of a protrusion array takengenerally along the reference lines A B, of FIG. 13.

FIG. 16 is a schematic illustration of a tunable laser constructed inaccordance with the present invention.

FIG. 17 is a schematic view of a tunable optical device constructed inaccordance with the present invention and using acoustic wave tuning.

FIGS. 18A, 18B are schematic drawings illustrating equivalent mirroraction for a one dimensional distributed feedback structure.

FIGS. 19A and 19B are schematic drawings illustrating the reflectingproperty of a two dimensional feedback structure constructed inaccordance with the present invention.

FIG. 20A is a schematic drawing illustrating mode locking forconventional lasers.

FIGS. 20B, 20C are schematic drawings illustrating mode locking for twodimensional feedback structures constructed in accordance with thepresent invention.

FIGS. 21A, 21B, 21C, 21D are schematic drawings illustrating theoperation of two dimensional periodic waveguide structures constructedin accordance with the present invention in which the directions oforientation of periodic variations make a non-orthogonal angle to eachother.

FIGS. 22A & B are diagrams showing the Bragg condition and thedispersion diagram respectively for a passive periodic waveguidestructure in accordance with the present invention.

FIGS. 23A & B are schematic diagrams showing a passive waveguide and atransmission characteristic for use as a stop-band filter.

FIGS. 24A & B are schematic diagrams showing combined pair of twodimensional distributed feedback structure constructed in accordancewith the present invention and coupled together in tandem together withthe combined transmission characteristic thereof useful as a pass-bandfilter.

BRIEF DESCRIPTION OF THE PREFERRED EMBODIMENTS If it and it; are thepropa ation vector for the two counter running waves with ,for theforward wave and k,, for the backward wave, then what is needed to makelaser action possible is to introduce a spatial perturbation in thewaveguide structure characterized by a reciprocal-lattice vector suchthat The physical meaning of E: becomes clear shortly. Take, as anexample, a waveguide structure with thickness variation in the zdirection having a period 0,. The reciprocal lattic vector for thisone-dimensional structure is simply =221r/a,. For distributed-feedbacklasers, the I; and I; vectors appear to be confined in a chosen plane(say the X2 plane) which is perpendicular to the plane of the wave-guidefilm. Thus, the period a, should be so chosen that a,='1r/k where k,=k,k,

In a layered waveguide structure, the value of k is bound by two limitsk n, k, k n, where n; if the index of refraction of the film, n, is theindex of refraction of the substrate or the top layer (the superstrate)whichever is larger, and k =2rrllt is the free-space wave number. Theselection of a proper value for 0 is restrained by the followingconsiderations. First, the gain of a laser material has a limitedbandwidth. That means, k can be varied only within a very limited range.Secondly, for effective waveguide structures, the difference between n,and n is only a few percent. For example, for polyurethane coated onmicroscope slide, we have nr-LSS and n,=l.5l. These two factors combinedimpose a very strict requirement on the value of a, Calculation showsthat a control of the period 0, within 1 2 percent is required for theGaAs- Ga,Al, ,.As laser system and a control of the period a within i0.05 percent is required for the Nd-dopedglass laser system.

A precise control of the period required of a onedimensionaldistributed-feedback laser limits the use fulness of thedistributed-feedback concept to laser materials with relatively broadgain profile. In my previous patent application, one of the schemes Iproposed was to have the wave vector k oriented away from the Gdirection so that a certain amount of tunability may be possible. InFIG. 1, the shaded grating represents the periodic perturbation in thewaveguide structure whose coordinate axes are y and z. whereas thedashed lines define the geometry of the pumped region whose coordinateaxes are y and z. In the chgsen coordinate systerns, thereciprocal-lattice vector G lies in the z direction and the laser beampropagates along the z direction in the waveguide.

For the laser configuration shown in FIG. 1, the Bragg condition forlaser feedback becomes k,,=%N,,Gsina, k,=%N,Gcosa Thus, the lasingwavelength must satisfy the following relation:

where N and N are two integers representing the order of Braggdiffraction involved in the feedback action. The question arises: whatphysical process can be used to generate a transverse distribution inthe y direction. It can be shown in semi-conductor lasers that pumpingcreates a spatial variation in the index of refraction which in turnestablishes mode patterns in the transverse direction, that is, the ydirection in FIG. 1. From Eq. (2) it is now seen that for a given perioda, we can vary a to satisfy the equation. In other words, it is possibleto adjust the orientation of the pump beam with respect to that of theperiodic structure so that the Bragg condition for feedback (which isessential in achieving laser action) can be satisfied at a certain hwithin the gain profile of the laser medium.

The above scheme has only limited usefulness for the following reasons.First, the same G appears in k, and 14,. Secondly, since the spatialdependence of refraction index on pumping is not understood, a preciseknowledge about k, and how to control it is not possible.

The present invention proposes to make periodic variations in more thanone direction in the plane of the film in order to achieve a precisecontrol of transverse modes. There are many ways to implement this idea.One simple way is illustrated in FIG. 2 where a wave guide structurewith thickness variations along two orthogonal directions (y and zdirections) is shown. In such a waveguide structure, the Bragg conditionfor feedback becomes where G,,=21r/a,,, G,=21r/a,, a and a, are theperiod of the thickness variation in the y and z direction,respectively, and N, and N, are two integers representing the order ofthe Bragg diffraction involved in the feedback.

FIG. 3 is a plot of the k, and It space based on Eq. (3). The verticallines represent all the possible values for k whereas the horizontallines represent all the possible values for k,,. Therefore, anyintersection represents a potentially allowable set of values for k, andk,. The exact determination ofthe operating condition of a thin filmlaser is illustrated in FIG. 4. At a given wavelength )t the magnitudeof the k vector is equal to k=k n, where k =21r/A is the free-space wavenumber. In other words, the operating points must land on a sphere ofradius k n It is further noted that the allowed values of k,, and k, arediscrete as they are given by Eq. (3). Therefore, the procedurue infinding the operating condition can be described as follows. We raise orlower the k,,k plane (FIG. 3) along the OC axis of the Ir n, sphericalshell (FIG. 4) until two points, such as P and 0, land on the sphere.The vector OP- =6Q specifies the values of k and k,, whereas the vectorGO specifies the values of k,. The k, value thus found must satisfy thefollowing equations:

and,

where (b is the phase at the film-substrate boundary, da is the phaseshift at the film top layer boundary, m is an integer representing themode number and W is the film thickness. This defines a discrete set ofvalues for k k,,, k as a function of m. A thin film laser with periodicperturbations in two directions of the film has all the three componentsof the k vector specified. In contrast, a thin film laser with periodicperturbation only in one direction of the film has only two of the threecomponents of the k vector specified.

Although the structure shown in FIG. 2 is used as an example toillustrate the laser operating principle, it is desirable in practicalapplication to consider structures different from that of FIG. 2. Theavailability of many G vectors for feedback also tends to make thestructure lossy. A laser beam, after igteracting with the periodicperturbations, will have a K vector given by a -0 where G,,= \"21r/a andG 2277/; are the two basis vectors in the reciprocal lattice, and a andu: are two integers, and y and 2 are the unit vectors in y and 2directions respectively. Eq. (I) is a special case of Eq. (5) and isused specifically for feedback. However, there are many possible Evectors. This is clear from FIG. 3. Suppose that the k state of a laserbeam is represented by the point P initially. The k state of thescattered light (that is the light created after the primary beaminteracts with the periodic perturbations) can be an intersection pointaway from P by any integral number of G and G The point T is such apoint. If the distance CT is smaller than Aim" where n" refractive indexof air, then the scattered light will not be totally reflected and canradiate into the surrounding air. Such a scattered mode is called theradiation mode. F IG. 5. shows the k k plane and the kiln" hemisphericalshell. The laser operating condition is represented by points P (theforward wave) and Q (the backward wave). The light scattered from theinteraction of the forward wave with the component of periodicperturbation having reciprocal-lattice vector r G G: is represented bythe point R. To be radiative, the point R must be below the Icon"spherical shell. In other words, the length CR must be smaller thanknn". Since there are many intersections in the l ,,k plane whichsatisfy the above conditions, there exist many radiative modes for thestructure shown in FIG. 2. Especially when the point R gets very closeto the kiln spherical shell. the radiative mode becomes very strong andthus the waveguide structure becomes very lossy. As will be discussedshortly, many important applications will require a small G compared toG As the value of 0,, decreases, the number of points (like R) beingclose to the km spherical shell increases and hence the waveguidestructure becomes increasingly lossy.

As will be shown later, in order to minimize the loss due to radiation,it is desirable that the two periodic perturbations be physicallyseparated from one another, or in other words, be made not to exist sideby side at the same time interface or in the same medium. Separationalso makes possible an independent control of the strength of they-directed and z-directed distributed feedback effects. An example ofseparate periodic perturbations is illustrated in FIG. 6 where aperiodic thickness variation in the z direction exists at the film toplayer interface and a periodic thickness variation in the y directionexists at the film substrate interface. A schematic representation ofthe substrate is shown in FIG. 7 where the uniformly spaced linesrepresent the periodic perturbations at the two interfaces. It is alsopossible that either or both periodic perturbations be made in the media(the substrate, the film and/or the top layer) instead of at theinterface. These alternatives were disclosed in my co-pendingapplication, Ser. No. 33 l ,675 previously referenced.

A schematic representation of another useful structure is shown in FIG.8 where periodic perturbations exist at the film top layer interface andin the substrate. Another useful structure is schematically illustratedin FIG. 9 where periodic perturbations exist at the substrate filminterface and in the top layer. In summary, a preferred combination oftwo periodic perturbations can be any one of the following combinations:(1 one periodic perturbation at the top layer film interface and theother periodic perturbation at the film-substrate interface, (2) oneperiodic perturbation at either of the two interfaces (top layer film orfilm substrate) and the other periodic perturbation in one of the threemedia (film, substrate, or top layer), (3) one periodic perturbation inone of the three media and the other periodic perturbation in either ofthe two remaining media.

There are many ways to introduce periodic perturbations at the interfaceand in the medium. A brief discussion of the presently available methodsnow follows by way of example. If a microscope slide is used for thesubstrate, then the slide can be first coated with a photoresist film.Subsequently, the photoresist film is exposed to an interference patternwith periodic regions of high and low light intensities, and after theexposure, the photoresist film is developed to produce a relief gratingon the microscope slide. Next, grooves are made into the slide eitherthrough etching by chemical reagents or through milling by ion beams.Finally, the photoresist film is removed from the slide, and the slideis coated with a film of chosen material for the waveguide. The finalproduct thus will have a periodic thickness variation at the filmsubstrate interface due to the periodic grooves. Similarly, periodicthickness variations can also be introduced at the top surface of thefilm, using laser beam lithography or electron beam lithographytechniques.

FIG. 10 is a schematic diagram illustrating how periodic perturbationscan be incorporated into the top layer, the film, or the substrate. Forexample, in the GaAs-Ga Al I .;As laser system, GaAs is used as the filmmaterial and Ga,Al. As is used as the substrate material. If periodicperturbations are desired in the top layer, a layer of SiO2 or ZnOmaterial is deposited on top of the GaAs film. Again, either chemicaletching or ion milling can be used to remove a part of the Si or ZnOmaterial in a pre-designed and periodic manner. The finishing laserstructure thus will have a top layer made of alternate and periodicregions of material B (SiO2 or ZnO) and material A (air) as illustratedin the top diagram of FIG. 10.

A periodic perturbation can also be created by an acoustic wave throughthe photo-elastic effect. A simple physical explanation for the effectmay be stated as follows. It is known that an acoustic wave createsalternately and periodically dense and rarefied regions. Since the indexof refraction is a function of both the atomic arrangement and thedensity in a given material, an acoustic wave will be accompanied by aperiodic variation in the index of refraction (as schematicallyillustrated in the bottom diagram of FIG. 10). It may be worthwhile topoint out that light beam is mostly confined in the film of a waveguidestructure, and penetrates only to a certain depth into the top layer andthe substrate. Therefore, the depth of periodic perturbation (d; for thetop layer and d, for the substrate as indicated in FIGS. 9 and 10) inthe top layer and in the substrate needs only to extend slightly beyondthe respective penetration depth in the two regions. That means d, andd, will have a value of the order of the wavelength of the laser beampropagating in the film. In certain thin film lasers such as the dyelaser, it is also possible to introduce periodic perturbations in thefilm itself. It is well known that a permanent change in the index ofrefraction will occur in photoresist materials if exposed to light, andpolymethylmethacrylate if exposed to energetic electrons. A film withperiodic index variations is schematically illustrated in the middlediagram of FIG. 10.

The superiority of thin film lasers having two separate periodicperturbations is best seen by referring to FIGS. 11 and 12. FIG. 11shows, as an illustrative example, the available values of k and k for acertain thin film laser. The larger circle represents the intersectionof the k n, spherical shell with the k k plane, whereas the smallercircle represents the intersection of the k n, spherical shell with thek,,k, plane. Points P and Q where the bigger circle runs through theintersection of the k,, and k lines represent the operating condition ofthe laser. For the example shown in FIG. 11, k =l .5 G for the forwardwave and k,=l .5 G for the backward wave. If the two periodicperturbations are othogonal, then points P and O which are symmetricallylocated with respect to P and 0 also meet the operating conditionrequirement. Therefore, from FIG. 11, k,,= -l.5 0,.

Two important questions regarding a thin film laser are its radiationloss and coupled-out signal. I-Iere distinction must be made between athin film laser with the two periodic perturbations being in the samelocation and a thin film laser with the two periodic perturbations beingin separate locations. As a specific example, it is assumed that thethin film laser represented in FIG. 11 has a periodic structure as thatshown in FIG. 2 with thickness variations in the y and z directionsexisting simultaneously at the film substrate boundary. Because of theavailgbility of many reciprocal lattice vectors G=N,,G,,+N,G, at thefilm substrate boundary, there exist many radiation modes such as pointsR R etc., lying within the smaller circle in FIG. 11. For example, alaser beam represented by the point P can be scattered to the point R,and thus be coupled out from the thin film waveguide. The existence ofmany radiation modes is undesirable for the following reasons. Asmentioned earlier, some of the modes may lie very close to the smallercircle and thus are strongly radiating. The strongly radiating modeseffectively increase the loss of the laser. It should also be pointedout that all the radiation modes represented by points R R etc.originate from the same laser beam and yet have different directions ofpropagation. In other words, a laser beam is simply scattered into manydirections. This is at variance with the original intention of thepresent invention that each light beam coupled out from a thin filmlaser constitutes a distinct channel operating at a differentwavelength.

In contrast to FIG. 11 a different situation is shown in FIG. 12 wherethe two periodic perturbations are separate from one another. As aspecific example, it is assumed that the thin film laser has a periodicstructure as that shown in FIG. 6 with the thickness variation in the ydirection existing at the film top layer boundary and the thicknessvariation in the z direction existing at the film substrate boundary.Insofar as the laser operating condition is concerned, the situationshown in FIG. 12 is identical to that shown in FIG. 11 if G, and G inthe two cases are the same. A laser beam propagating in the filmexperiences the combined effects of (3,, and 6,. Therefore, the laseroperation condition is still represented by the points P and Q and thepoints P and However, insofar as the radiation loss and coupledoutsignal are concerned, the situation for FIG. 12 is quite different fromthat for FIG. ll. When a laser beam hits the film top layer boundary,the only reciprocal-lattice vectors available for the spattering processare those in the y direction, that is, G=N,,G,,. In other words, thepoints P and P can only be scattered to P P etc., whereas the points 0and Q can only be scattered to Q1, Q etc. Since all the points P P,,etc., and Q1, Q etc., are outside the smaller circle, none of thescattered light can radiate out from the thin film waveguide. When alaser beam hits the filfm substrate boundary, thet only reciprocallattice vectors available for the sgattering process are those in the zdirection, that is, G=N,G,. The points R R R and R in FIG. 12 representall possible radiation modes of the laser, which are the same as thosein a corresponding onedimensional distributed feedback laser. Therefore,the radiation loss in a two dimensional distributed feedback laser canbe reduced to a minimum amount equal to that in a correspondingone-dimensional distributed feedback laser if two separate periodicperturbations are used in the two dimensional laser.

The characteristics of a two-dimensional DFB laser can be summarized asfollows. Owin to the availability of many reciprocal lattice vectors theoutput will show multiple modes oscillating simultaneously. However,each laser mode is expected to show a very narrow spectral width and asharply defined direction owing to the additional selection for thevalue of k,,. Such a two-dimensional DFB laser offers a definitepossibility as a source for multichannel operation in an in tegratedoptical system. The laser medium for multichannel operations should havea relatively broad spontaneous emission-band width. Semiconductors andorganic dyes are natural candidates for such purposes.

We should also point out that a DFB scheme based on a two dimensionalperiodic waveguide structure should be extremely useful in achievinglaser action in materials with relatively narrow spontaneous emissionband. The main difficulty with these materials is the precise controlrequired of the period so that the Bragg wavelength A will fall withinthe gain profile of the laser medium. In a two-dimensional DFB laser, wecan make a much bigger than a and thus use 0,, as a fine control for G.For thickness variations made through chemical etching, the etchedgrating can be made almost rectangular in shape; hence the periodicchange in the longitudinal wave number is better approximated by arectangular spatial dependence than a sinusoidal spatial dependence. Itis well known that a rectangular wave has rich harmonic contents whichdrop off as l/q where q is the order of the spatial harmonic. For a 0.9pm gelatin film deposited on a quartz substrate, a 10.05 1.1m thicknessvariation results in a feedback coefficient of the order of 200 cm forthe first order Bragg scattering. For the 9-th spatial harmonic, thefeedback coefficient is expected to be around 22 cm, a value generallysufficient to cause laser action. We can further increase the number ofpossible G vectors by making the periodic lattice in the shape of aparallelogram instead of a rectangle. Using a two-dimensional obliquegrating structure of unequal periods and working with high spatialharmonics, one may be able to extend the usefulness of the distributedfeedback concept to laser materials with narrow emission band, such asNd-doped glass or Nd-activated lanthanum oxysulfide.

In the following discussion, experimental results on two-dimensionalthin-film DFB dye lasers is reported. A microscope slide was coated withKodak KOR photoresist. The coated photoresist film was then exposed toan interference pattern produced by an argon laser at 0.488 pm. Afterthe period of the interference pattern was readjusted and theorientation of the microscope slide was turned by around an axis normalto the slide, the photoresist film was again exposed. Development of thephotoresist film left a twodimensional relief grating on the microscopeslide. Subsequent chemical etching produced two-dimensional grooves ofabout 0.1 pm deep into the SiO substrate. The periods a, and a; of theetched grating structure were determined by diffraction experiments. Fornormal incidence one has a,,=)t[ l (2d/y) &and a similar expression fora where y is the separation measured between the two maxima ofdiffracted light closest to the origin and at a distance d from thegrating. Of the several gratings made, the one used in the experimentreported here has the following set of values: a,,=4.34 um and a,=0.635pm.

The etched microscope-slide substrate, after the photoresist wasremoved, was coated with polyurethane doped with rhodamine 6G to a filmthickness W around 0.8 pm For a mode to be confined in a waveguide witha substrate index n, and a film index n;, we must have n,k k,, n,k whichsets an upper limit for k With a value for W chosen to be below lptm,the waveguide can support only the fundamental (m=0) mode in the xdirection. A N laser beam focused by a cylindrical lens was used to pumpa narrow strip of the film about 2 cm long. The amount of pumping powerdensity was varied by changing the focal position of the lens. Above acertain threshold density of pumping power, laser action took place witha strong emission around 0.642 In. This strong emission was accompaniedby the appearance of mode structure in the laser beam.

For the two dimensional DFB laser reported here, third order Braggscattering was utilized to produce the necessary feedback between theforward and backward running waves. If we assume that the light weobserved in the experiment was diffracted out of the film throughfirst-order Bragg scattering by interaction with the grating in the zdirection, then the diffracted light would have a'k v ctor with itscomponents in the yz direction given by k',,,=j20.5N,,G,,+2(l.5-l) GThus the angle 0 between the z-directed light spot (N,,=0) and eitherone of the two adjacent spots (N,,-J:l) is expected to be tan (G,,/G,)or tan "(0.147). The experimentally observed value for 6 is tan"(0.146).

The value of k,. can be calculated from Eq. (40). Using k Ek and W=O.85pm, we find k ,=0.l8 k Thus, the theoretical laser-wavelength A is 0.645pm for the fundamental transverse mode with N,,=0. The separation Alt inwavelength for transverse modes with nonzero N, from the N,,=0 mode isapproximately equal to AA/)t=0.5(N,,A/2n,a,,) The calculated values are:A)I=7.5A for N,,=.Ll Alt=*-30 A for N,,=i2, and Alt=-67 A for N,,= L3.Experimentally, the observed laser emission spectrum consists of severalsharp lines centered around 0.642 um and with a maximum separation aboutIOO A. These observations are in general agreement with the theory.

In the experiment reported here, the two sets of periodic perturbationsare at the same location, namely at the film substrate boundary. Thatmeans, reciprocal lattice vectors available for coupling laser beam outof the film are, in general, two dimensional vectors containing both yand 1 components. As a result, a given transverse mode can be scatteredout from the film to appear in different orientations through itsinteraction with reciprocal lattice vectors with different N, and thecoupled out laser beam actually consists of several transverse modeswith different N In principle the situation can be remedied by using twoseparate sets of periodic perturbations in different locations, forexample, one at the film substrate boundary and the other at the filmtop layer boundary. Insofar as the distributed feedback effect isconcerned, the available G's are kept two-dimensional. However, thegratings at the two boundaries are now made one dimensional.

One interesting extension of the foregoing experiment is to have twoseparate periodic structures for two dimensional DFB lasers, one beingin the superstrate oriented in the z direction and the other being inthe substrate oriented in the y direction. For the y-directed spatialvariation, we can use acoustic waves with frequency in the Hz range tocreate an index variation with a pm spacing. By varying the acousticfrequency (used as a fine tuning) and by changing the axis of thepumping beam (used as a coarse control), it is expected that we can haveDFB thin film dye layers tunable almost continuously over a widewavelength range.

In the waveguide structures presented in the foregoing discussion, twodimensional feedback effect is produced by two sets of line gratingsoriented in different directions in a plane or in spaced planes parallelto the plane of the waveguiding film. Since reflection from a linegrating is directed toward a specific direction, the two dimensionaleffect produced thereby is actually a superposition of two linear (onedimensional) effects. In the following discussion an alternate anddifferent way of achieving two dimensional feedback effect is presented.For illustrative purposes, a waveguide with two dimensional array ofscattering perturbations is shown in FIG. 13. In contrast to thestructure shown in FIG. 2 where the perturbations are caused by paralleland straight grooves, the structure shown in FIG. 13 has its structuralchange caused by isolated perturbations such as hollows (FIG. 14) orprotrusions (FIG. 15) which are arranged in a periodic manner in a twodimensional array as in FIG. 13. In this structure, each hollow (or eachprotrusion) acts as a scattering center. If the cross-section of eachhollow (or protrusion) is nearly circular in shape, then each scatteringprocess is almost isotropic, having nearly equal strength in alldirections in the yz plane. Therefore, diffraction of a light beam bysuch dot array structures is very much similar to diffraction of anX-ray by an atomic structure insofar as the diffraction property in thetwo dimensional yz space is concerned. The light reflected from theplane A 3, in FIG. 13 is expected to be nearly as strong as the lightreflected from the plane A B In contrast, for the grid-like structure ofFIG. 2, the light reflected from planes parallel to the grating isexpected to be stronger than the light reflected from other planes.

The periodic structures of both FIG. 13 and FIG. 6 possess twodimensional properties which can be used in active as well as passivethin film optical devices. The structure of FIG. 13 is easier tofabricate than that of FIG. 6. The former also provides distributedfeedback of nearly equal strength from different reflecting planes. Atwo dimensional laser using a dot array structure is expected,therefore, to give laser outputs of nearly equal strength as thelongitudinal direction of the pumping beam is rotated in a tunable laserto select different sets of G in Eq. (I). The tunability of such a lasercovers a wide wavelength range. On the other hand, the structure of FIG.6 has a great deal of flexibility. For example, the strengths of they-directed and zdirected feedback effects can be independentlycontrolled by making d, and d, different. A laser operated with a fixedN but different N 's can be made to give transverse modes with nonzero Ns of nearly equal strength as the fundamental mode with N =0 by using alarge d, so that the y-directed feedback effect is strong. A laser usingthe structure of FIG. 6 can also be tuned electrically if one set ofperiodic perturbations is caused, for example, by an acoustic wave.However, such electric tumability which is possible only with linegratings is expected to cover a relatively narrow wavelenght range. Fromthe above discussion, it seems that the structures of FIG. 13 and FIG. 6will complement each other in their usefulness in thin film opticaldevices.

The foregoing discussion concerning two dimensional dot arrays and twodimensional gratings serves to illustrate that the invention disclosedherein can be implemented by many structures. In general, manystructures having a two dimensional periodicity are known from work onreticles (graticules) wherein such doubly periodic structures are usedfor distance measurements. Many such systems of dots, line, or partialline nets can form the geometrical basis of the perturbations requiredin the present invention.

In the foregoing discussion, it is shown that a thin film laser with twoseparate periodic perturbations can be as efficient as a thin film laserwith a single periodic perturbation. It is the purpose of the followingdiscussion to show the many important applications of thin film lasershaving two separate periodic perturbations. For ease of discussion, theapplications of the present invention are divided into two categories.The first category applies to materials where it is necessary to use twoperiodic perturbations in order that the concept of distributed feedbackmay succeed. The second category applies to materials where using twoperiodic perturbations will provide new and useful applications whichare not possible with a single periodic perturbation.

So far, the concept of distributed feedback has been successfullyapplied only to dye lasers. Thin film dye lasers have been madeoperative by using periodic thickness variations to provide thenecessary feedback. The reason for easy success with dyes is that dyeshave a very broad and strong emission band, and as a result, incondition for laser oscillation can easily be satisfied. There are manyimportant laser materials which have a narrow emission band. Forexample, rare-earth doped glass has a spontaneous emission bandwidth ofthe order of 30 A, GaAs-Ga Al As semiconductor heterojunction has aspontaneous emission bandwidth of the order of 100 to 200 A. For lasermaterials with spontaneous emission bandwidth about or below 100 A, anaccurate control of the physical dimensions of a thin film laser, mainlythe thickness of the film and the period of the thickness variation,becomes essential. For a thin film laser using first order Braggscattering for distributed feedback, a spontaneous emission bandwidth of100 A simply means that the period of the thickness variation has to becontrolled within a tolerance of 30 A in a film with index of refractionn;=l.67 and within a tolerance of IS A in a film with index ofrefraction n,=3.34. Such a tight tolerance makes it difficult to makethe appropriate periodic structure for the one dimensional periodicperturbation thin film laser. Using two periodic perturbations greatlyrelaxes the tolerances in the values of a and a,,.

For a thin film laser with two orthogonal periodic perturbations, thewavelength condition is where kg is the guided wavelength in the film.Let 0,.

=a +Aa and a,=a, +Aa, where A0,, and An, are the re- 25 where Alt is thespontaneous emission bandwidth. If a is made much larger than a say a,,=la, a much larger Ad /aw than Ara/a by a factor of about 100, can betolerated such that Eq. (7) is satisfied within the spontaneous emissionbandwidth Alt. Eq. (6) also shows that if a,, a,, the term ('n'N,,/a,,)can be used as a fine tuning to satisfy the wavelength condition. Byusing different values of N, in Eq. (6), it is possible to compensatefor the error caused by an inaccurate value of a, In other words, evenifa, is away from the desired value by a value much larger than A, therewill be at least one waveguide mode (with a definite set of N, and N,)which may satisfy Eq. (7). The term (N m'la makes up the difference.This added flexibility by using two periodic perturbations greatlyrelaxes the tolerances on the values of a, and 0,, and this relaxationis extremely useful for laser materials with a narrow spontaneousemission band.

Among the many new applications which are made possible by using twoseparate periodic perturbations is the tunability of a thin film laser.From Eq. (6) it is obvious that the laser wavelength A can be changed byusing different values of N, and N, A practical arrangement is shown inFIG. 16 in which a cylindrical lens 17 is used to focus the pumpinglight into a long and narrow beam 18 impinging on a double periodicstructure 19 as disclosed herein. in other words, the pumped region hasa rectangular geometry similar to the one shown in FIG. I. as defined bythe dashed lines. Because of the geometry of the pumping beam, onlythose modes are favored which have the projection of the k vector in theyz plane nearly coinciding with the long direction of the rectangle.Therefore, by rotating the axis of the cylindrical lens, the longdirection of the pumping beam is changed and thereby a different set ofvalues for N, and N, is favored in Eq. (6) for laser action.

The lasing wavelength can also be tuned by varying the period a, or awhichever is larger while holding the smaller period fixed. As aspecific example, it is assumed that a fixed periodic perturbationexists in the z direction at the film top layer boundary and a variableperiodic perturbation in the y direction exists in the substrate. Thevariable periodic perturbation is caused by an acoustic wave propagatingin the substrate along the y direction. The period 0,, thus can bevaried by changing the frequency of the acoustic wave. The acousticvelocity in most materials is of the order of 2X l0-"cm/sec. For a,,=20microns, the frequency of the acoustic wave is about 10 cycles/sec.Practical methods are available for generating acoustic waves in themicrowave region with frequency in the neighborhood of 2X 10 cycles/secor below. The techniques of acoustic beam steering are well establishedand can be useful in the present application. In FIG. 17, an array ofacoustic transducers 21, 22, 23 is shown. By changing the relative phaseof the acoustic wave generated by each transducer, the direction of theacoustic wavefront can be varied. If the phase of the acoustic wave isadvanced progressively from transducer 23 to transducer 21, then theacoustic wavefront is steered toward the left as illustrated in FIG. 17.On the other hand, if the phase of the acoustic wave is retardedprogressively from transducer 23 to transducer 21, then the acousticwavefront is steered toward the right. Since the directiogof theacoustic wavefront represents the digection o G, in the present context,the angle between G, and

can be varied by changing the relative phase of the acoustic wavesgenerated in each transducer. It should be pointed out that periodicvariations in the property of a waveguide (the substrate, the film, orthe top layer) can also be produced by means other than acoustic waves.In ferroor ferri-magnetic materials, the size of magnetization domainscan be controlled by a biasing magnetic field. In ferroelectricmaterials, the size of electric-polarization domains can be varied by anapplied biasing electric field. ln nematic liquid crystals, grating-likedomains (known as Williams domains) of alternate values of index ofrefraction are formed if an electric field applied across the liquidcrystal exceeds a certain threshold value. The period of thegrating-like domains can be varied over a wide range (from 5 microns to60 microns) either by changing the frequency of the applied electricfield if the liquid crystal is operated in the Williams-domain mode orby changing the value of the applied electric field if the liquidcrystal is operated in the variable-grating mode. In cholesteric liquidcrystals, a dilation of the pitch of the helix molecular structureresults upon the application of an electric field. The pitch can cover arange from 0.2 micron to 20 microns, depending on the choice ofcholesteric liquid crystals. Once a cholestric liquid crystal is chosen,the pitch and hence the value of a, in Eq. (6) can be varied eitherbychanging the applied electric field or by changing the ambienttemperature.

Another important application which is made possible by using twoseparate periodic perturbations is for multi-channel operation of a thinfilm laser. If 0,, is made much larger than a in Eq. (6), then waveguidemodes with the same N but different N, will have only slightly differentwavelength. For a thin film DFB (distributed feedback) laser having asingle periodic per turbation, the coupled out signal appears as aprojected line (the so-called mode-line or m-line) because only thevalues of k and k, are specified. For a thin film DFB laser having twoperiodic perturbations, the coupled out signals are lines projected asdots because all the components k,,-, k, and k are specified. Each dothas a different set of k,, k,,, and k Therefore, when the lasing modesare coupled out from the periodic thin film waveguide (either by agrating coupler or a prism coupler), each mode will have a distinctdirection of propagation and a distinct wavelength. These features arenot only useful but also necessary for multi-channel operation of athin-film DFB laser.

The simultaneous lasing of several transverse modes of slightlydifferent wavelengths makes possible the operation of a scanning laserbeam. It has been demon strated with conventional lasers that if themany transverse modes of a laser are made to oscillate with a definitephase relationship, then the combined effect of all the transverse modesproduces a laser beam which travels back and forth in the transversedirection as a function of time. The technique of making different modesto oscillate with defininte phase relationship is called mode-locking.It should be pointed out that there are also longitudinal modes (see mypreviously referenced applications, Ser. No. 296,178 and 331,675) in athin film laser and the longitudinal modes can also be phase locked. Iftransverse and longitudinal modes are simultaneously locked in phase,then the light energy can be confined to a small region in space andtravels a zig-zag path as it reflects back and forth in the lasercavity.

In order to see how practical arrangements can be made for mode lockingin thin film lasers, the following observations are made. FIG. 180 showsschematically a thin film DFB laser having a single set of periodicperturbations in the z direction. As mentioned earlier, theperturbations provide periodic reflections in the a direction andthereby serve as function similar to that of mirrors in conventionallasers. Further, the analysis presented in my previously referencedapplication Ser. No. 296,178 shows that a very high reflectivity can beachieved with periodic structures which far exceeds the reflectivityachievable with mirrors. However, since reflections are possible only inthe zi direction for the structure of FIG. 18a, a single set of periodicperturbations behaves somewhat like plane parallel mirrors. Asillustrated in FIG. 18b, a set of plane parallel mirrors is basicallyonly marginally stable. Only laser beams propagating in a di ectionperpendicular to the mirrors (as indicated byiG) will be bounced backand forth in the resonator without suffering diffraction losses. Anybeam propagating in a direction away from- (as indicated by the dashedarrows) will have very high difiraction losses. Therefore, a DFB laserwith a single set of periodic perturbations is unsuitable as planeparallel mirrors are unsuitable in many practical applications of knownlasers.

The fact that using two sets of periodic perturbations can overcome thedrawback of a single set of periodic perturbations can best be seen fromFIGS. 19a and 19b.

As shown in FIG. 140, a DFB laser with two sets of periodicperturbations has, in addition to the reflecting planes 1 as in a DFBlaser with a single set of periodic perturbations many other reflectingplanes such as those marked by 32, 32, 33 and 33'. A laser beampropagating in a direction perpendicular to any set of the reflectingplanes will be bounced back and forth in the resonator without sufferingdiffraction losses. FIG. 19b shows schematically several configurationsin which a laser beam can be reflected back and forth. There are manyother possible configurations for reflection which are not shown in FIG.19b. Therefore, a DFB laser structure with two sets of periodicperturbations provides many stable configurations for reflections totake place, and in that sense behaves in a manner analogous to sphericalmirrors or the equivalent so that many transverse modes may oscillatesimultaneously.

FlG. 200 shows schematically one arrangement for mode locking aconventional laser beam. The essential element in the arrangement is anintercavity region 41 in which either the loss or the phase of a laserbeam can be modulated. The basic principle of mode locking can easily befound in the literature, and can be briefly stated as follows. If theloss or phase of the intercavity space 41 is modulated at a regularfrequency coresponding to the intra-mode spacing, then all the modes areforced to oscillate with a definite phase relationship because laserbeams oscillating with a different phase will experience a high loss (ora low gain). The high loss (or low gain) is either a direct result ofthe loss introduced into the cavity in the case of loss modulation or anindirect result of shifting the wavelength of a laser beam outside thegain profile in the case of phase modulation. The loss or phasemodulator can be roughly visualized as a gate which allows the passageof a light beam at regular time intervals. This regular opening of agate forces all the modes to pass the gate at a definite time interval,thereby regulating the phase of all the laser modes. It should bepointed out that under cetain conditions, the nonlinear effects of thelaser medium itself may cause a fixed phase relationship to bemaintained between the oscillating modes. The phenomenon is known asself-locking. For selflocking, no inter-cavity loss or phase modulatoris needed.

FIG. 203 shows schematically one possible arrangement for mode-lockingin thin film DFB lasers, and FIG. 20C shows the actual laser structurefor use in the arrangement. The two regions marked by A and B areregions with periodic perturbations, and thus correspond to the twomirrors in the conventional laser (FIG. 20A). The region C is used forinternal modulation of the loss or the phase of the laser beam. Itshould be pointed out that modification of the scheme shown in FIG. 20Band C are possible and may be necessary under certain circumstances.First, in laser media where non-linear effects are sufficient to causeselflocking, the region C is no longer necessary and hence can beeliminated. Second, under certain circumstances it is neither necessarynor desirable to separate the two regions A and B; or in other words, dshould be set equal to zero in FIG. 20B and C. Accordingly to theanalysis presented in my previous patent applications Ser. No. 296,178,and Ser. No. 331,675, the gain in a DFB laser depends on how far theguided wavelength )t,,=2*rr/k is away from the Bragg conditionk,=N,G,/2. Consider an arrangement in which d=0 and an electric fieldexists in the region C. The applied electric field modulates the gain inthe region C as it changes K, through the electro-optic effect. Thus,for d=0, modulation of the gain can be used for mode-locking. On theother hand, ifd O, the phase of a laser beam is modustances, more thantwo periodic perturbations may be needed. The main difference betweenorthogonal and oblique configurations is the intra-mode spacing. For a,,a an expansion of Eq. (6) shows that the wavelength spacing betweenN,,+l and N, modes is proportional to (N,,+l Nf. Therefore, theintra-mode spacing Mu -h, is not a constant independent of j=N However,the difference between )t, ,i\ and A k, is proportional to (N,,+l --2N,,which reduces to a constant independent of N,,. The situation is verysimilar to that existing between the transverse modes in semiconductorheterojunction lasers. For such cases, the frequency of the loss (orphase) modulator must be so chosen that it corresponds to the wavelengthspacing A, ,+)t, ,2 A Mode locking of these transverse modes involvesthe combination tone produced by the non-linearity of the laser medium,and hence is a second-order effect.

For DFB lasers having oblique periodic perturbations, the situation isquite different. FIG. 21a shows an example for which G, makes an angle90-a with The wavelength condition for this situation is whereG,=21r/a,, and G,=2rrla,. For a,, a,, Eq. (8) can be approximated by Anexpansion of Eq. (9) shows that the intra-mode spacing A -It, isproportional to 0+1 )j=l which is a constant independent of FN,,.Therefore, phaselocking the transverse modes in DFB lasers with obliqueperiodic perturbations is quite similar to phaselocking the transversemodes in conventional gas lasers. The frequency of the loss (or phase)modulator is so adjusted that it corresponds to the intra-mode spacing AA which is the same for any pair of adjacent modes.

To support a pair of transverse modes with :N,, in Eq. (9), it may benecessary that a pair ofi complementary to as shown in FIG. 21B be madeavailable. The periodic structure which will provide both 1%,, and 1G,,,is schematically shown in FIG. 21C. Besides the set of periodicperturbations in the z direction, there are two other sets of periodicperturbations marked by (I) antLUI). The set (I) providesreciprocallattice vectors N G, whereas the set (ll) providesreciprocal-lattice vectors N G FIG. 21D shows the projection of the kvector in the yz plane for the transverse mode with N,,=l (or N,,,=l)and N,= *-l. and for the transverse mode with N,,=l (or N,,,=l andN,=tl. If the angle a in FIG. 21C is made equal to zero, then the twosituations shown in FIG. 21D become identical. For a 0, the degeneracyis removed, and the structure shown in FIG. 21 will split a pair ofdegenerate modes into two nondegenerate transverse modes with slightlydifferent frequencies. In summary, the main effects of using obliqueperturbations are that the wavelength spacing A rA, between two adjacentmodes is independent of the mode number j-N,, and that the number ofindependent modes is increased almost by a factor of two by the removalof degeneracy. In practical applications, this means that the number ofresolvable spots is increased by a factor of two in a scanning laser.

A passive waveguide with two or more sets of periodic perturbations canalso be used to perform certain passive device functions such asfiltering and modulatinga laser beam. (The word passive" is used torefer to materials, structures, or devices without gain.) Thereciprocal-lattice vectors G associated with two arbitrary sets ofperiodic perturbations can be expressed in a general form:

where N and N, are two integers, and a, and a are the periodicity of theperturbation in the y and z direction, respectively. In general, the twounit vectors 7 and 2 need not be orthogonal; therefore, Eq. I0) isapplicable to oblique as well as orthogonal perturbations.

It is well known in the energy-band theory of solids thatforbidden-energy gap (stop band) appears in the energy versus 1: diagramin a penlgdic lattice. Similarly a laser beam propagating in the Gdirection will see a stop band in a passive periodic waveguide. In ageneralized coordinate system, the Bragg condition for collinearinteraction is given by lGl=2k,,,, as shown in FIGS. 22 where lGl is themagnitude of the vector and k,,, is the projection of the wave vector kupon the yz plane. Therefore, the center wavelength A, of the stop bandis determined by the Bragg condition A,,=41r/ lGl where )t,,=2*rrlk,, isthe guided wavelength. Furthermore, the stop band has a finite bandwidthAll which can be pre-determined by controlling the depth of the periodicperturbation, for example, the values of d, and d in FIG. 2. A laserbeam with a wavelength falling in the stop band will be totallyreflected. FIGS. 23A and 23B whow schematically a passive waveguide andits transmission characteristic. Depending on the wavelength of anincident beam, the beam will be either reflected back (indicated by thearrow A) or transmitted through (indicated by the arrow B) thewaveguide. 0bviously, a waveguide with two sets of periodicperturbations can be used as a stop-band filter. When two suchwaveguides having different and nonoverlapping bands as shown in FIGS.24 are connected in tandem, they can be used as a pass-band filter.

1. A thin film optical device comprising an optical waveguide havingboundary surfaces and defining a guided wavelength for propagating waveof light at a predetermined frequency and guided wavelength therein,said waveguide having a predetermined optical index of refraction andmade of a material transparent to light of said predetermined frequency,means defining at least one boundary layer adjacent to said waveguidesuch that the propagating wave for light at said predetermined frequencyextends botH within said waveguide and into said boundary layer, saidboundary layer having one or more indices of refraction of saidwaveguide, perturbation means associated with said boundary layer andsaid waveguide for forming a first periodic variation of the index ofrefraction thereof in a first predetermined direction, said firstperiodic variation causing a spatial variation of said index ofrefraction between two values which repeat in a regular pattern of afirst predetermined periodicity ay, said perturbation means furtherforming a second periodic variation of said index of refraction in asecond predetermined direction and causing a spatial variation of saidsecond periodic variation between two values which repeat in regularpatern of a second predetermined periodicity az.
 2. A thin film opticaldevice as in claim 1 in which said means forming said periodicvariations comprises a two dimensional array of scattering centers.
 3. Athin film optical device as in claim 2 in which said perturbation meansincludes a first array of reflective linear elements forming a firstgrating and a second array of reflective linear elements forming asecond grating.
 4. A thin film optical device as in claim 1 in whichsaid first and second periodic variations are orthogonal to each other.5. A thin film optical device as in claim 1 in which said first andsecond periodic variations are oblique to each other.
 6. A thin filmoptical device as in claim 1 wherein periodicities ay and az satisfy therelation
 7. A thin film optical device comprising an optical waveguidehaving boundary surfaces and defining a guided wavelength forpropagating wave of light at a predetermined frequency, said waveguidehaving a predetermined optical index of refraction and made of amaterial transparent to light of said predetermined frequency, meansdefining one or more boundary layer adjacent to said waveguide such thatthe propagating wave for light at said predetermined frequency extendsboth within said waveguide and into said boundary layer, said boundarylayer or layers having one or more indices of refraction at least aportion of which is less than the index of refraction of said waveguide,first perturbation means associated with said boundary layer, saidwaveguide or the interface between said boundary layer and saidwaveguide for forming a periodic variation of the index of refractionthereof in a first predetermined direction, said periodic variationbeing arranged for causing a spatial variation of said index ofrefraction between two values which repeat in a regular pattern in apredetermined periodicity ay, second perturbation means associated withone of said boundary layers and waveguide or the interface of saidboundary layer and said waveguide for forming a periodic variation ofthe index of refraction thereof in a second predetermined direction,said second periodic variation being arranged for causing spatialvariation of said index of refraction between two values which repeat inregular pattern of a second predetermined periodicity az wherein
 8. Adevice in claim 7 further including generator means for applying anacoustic field to said boundary layer and means for varying thefrequency of the output of said generator.
 9. A device as in claim 7further including an ultrasonic generator coupled to said boundary layerand means for varying the frequency output of said generator.
 10. Adevice as in claim 7 wherein said boundary layer has an index ofrefraction variable in response to an applied electric field and furtherincluding means for applying an electric field to said layer, means forvarying the strength of said field.
 11. A device as in claim 7 whereinsaid boundary layer has an index of refraction variable in response toan applied magnetic field and further including means for applying amagnetic field to said layer, means for varying the strength of saidfield.
 12. A device as in claim 7 wherein said boundary layer has anindex of refraction variable in response to an applied acoustic standingwave pattern, and further including means for extablishing an acousticstanding wave pattern in said layer.
 13. A thin film optical devicecomprising an optical waveguide having boundary surfaces and defining aguided wavelength for propagating wave of light at a predeterminedfrequency, said waveguide having a predetermined optical index ofrefraction and made of a material transparent to light of saidpredetermined frequency, means defining at least one boundary layeradjacent to said wave-guide and in such proximity that the propagatingwave for light at said predetermined frequency extends both within saidwaveguide and into said boundary layer, said boundary layer having oneor more indices of refraction at least a portion of which is less thanthe index of refraction of said waveguide, perturbation means associatedwith said boundary layer, said waveguide or the interface between saidboundary layer and said waveguide for forming a first periodic variationof the index of refraction thereof in a first predetermined direction,said periodic variation being arranged for causing a spatial variationof said index of refraction between two values which repeat in a regularpattern of at least one first predetermined periodicity ay, saidperturbation means further forming a second periodic variation of theindex of refraction thereof in a second predetermined directiondifferent from said first direction, said second periodic variationvarying between two values which repeat in regular pattern of at leastone second predetermined periodicity az.
 14. A thin film optical deviceas in claim 13 wherein said first and second periodic variations arescattering centers located at the intersections of a pair ofcrossed-gratings.